{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "least_sqaure_method.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.4"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gjQwmKjeF7QD",
        "colab_type": "text"
      },
      "source": [
        "原文代码作者：https://github.com/wzyonggege/statistical-learning-method"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NApZAFWwF7QE",
        "colab_type": "text"
      },
      "source": [
        "# 第1章 统计学习方法概论"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NfyC6OorF7QF",
        "colab_type": "text"
      },
      "source": [
        "高斯于1823年在误差e1 ,… , en独立同分布的假定下,证明了最小二乘方法的一个最优性质: 在所有无偏的线性估计类中,最小二乘方法是其中方差最小的！"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SgzwlgxJF7QF",
        "colab_type": "text"
      },
      "source": [
        "### 使用最小二乘法拟和曲线\n",
        "\n",
        "对于数据$(x_i, y_i)(i=1, 2, 3...,m)$\n",
        "\n",
        "拟合出函数$h(x)$\n",
        "\n",
        "有误差，即残差：$r_i=h(x_i)-y_i$\n",
        "\n",
        "此时L2范数(残差平方和)最小时，h(x) 和 y 相似度最高，更拟合"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nEy9BM0kF7QG",
        "colab_type": "text"
      },
      "source": [
        "一般的H(x)为n次的多项式，$H(x)=w_0+w_1x+w_2x^2+...w_nx^n$\n",
        "\n",
        "$w(w_0,w_1,w_2,...,w_n)$为参数\n",
        "\n",
        "最小二乘法就是要找到一组 $w(w_0,w_1,w_2,...,w_n)$ 使得$\\sum_{i=1}^n(h(x_i)-y_i)^2$ (残差平方和) 最小\n",
        "\n",
        "即，求 $min\\sum_{i=1}^n(h(x_i)-y_i)^2$\n",
        "\n",
        "----"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R2XNNYriF7QH",
        "colab_type": "text"
      },
      "source": [
        "举例：我们用目标函数$y=sin2{\\pi}x$, 加上一个正太分布的噪音干扰，用多项式去拟合【例1.1 11页】"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PXDy36yGF7QH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import scipy as sp\n",
        "from scipy.optimize import leastsq\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yR6efbDhF7QK",
        "colab_type": "text"
      },
      "source": [
        "*ps: numpy.poly1d([1,2,3])  生成  $1x^2+2x^1+3x^0$*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OTfmbWPEF7QL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 目标函数\n",
        "def real_func(x):\n",
        "    return np.sin(2*np.pi*x)\n",
        "\n",
        "# 多项式\n",
        "def fit_func(p, x):\n",
        "    f = np.poly1d(p)\n",
        "    return f(x)\n",
        "\n",
        "# 残差\n",
        "def residuals_func(p, x, y):\n",
        "    ret = fit_func(p, x) - y\n",
        "    return ret"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WttTJrBKF7QO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 十个点\n",
        "x = np.linspace(0, 1, 10)\n",
        "x_points = np.linspace(0, 1, 1000)\n",
        "# 加上正态分布噪音的目标函数的值\n",
        "y_ = real_func(x)\n",
        "y = [np.random.normal(0, 0.1)+y1 for y1 in y_]\n",
        "\n",
        "def fitting(M=0):\n",
        "    \"\"\"\n",
        "    M    为 多项式的次数\n",
        "    \"\"\"    \n",
        "    # 随机初始化多项式参数\n",
        "    p_init = np.random.rand(M+1)\n",
        "    # 最小二乘法\n",
        "    p_lsq = leastsq(residuals_func, p_init, args=(x, y))\n",
        "    print('Fitting Parameters:', p_lsq[0])\n",
        "    \n",
        "    # 可视化\n",
        "    plt.plot(x_points, real_func(x_points), label='real')\n",
        "    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')\n",
        "    plt.plot(x, y, 'bo', label='noise')\n",
        "    plt.legend()\n",
        "    return p_lsq"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wY_bWzumF7QQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "bd3a2cf6-a1f8-4e47-f27a-e80fb9e75aae"
      },
      "source": [
        "# M=0\n",
        "p_lsq_0 = fitting(M=0)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting Parameters: [0.00164123]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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1rQ6nQo0YATNm2GoIIrb7GTNKXxeiTvVgXrujHTuPnGXStztcH6xSPsYZiSEdiCz2PMK+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\ngg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qc2MNMCeF7QU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "21149ca9-e072-454c-fb43-7c6c98139dcd"
      },
      "source": [
        "# M=1\n",
        "p_lsq_1 = fitting(M=1)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting Parameters: [-1.30031388  0.65179817]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wm1QN1n0IN/JGQbrhrSqTnCKZtiNM71AURTdGSQxCiPZCiDNCiDAhxKh03v9A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\njiZLgdUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "csiTfCLnF7QX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "da045a19-21f5-49db-a6c1-b930cc4adebc"
      },
      "source": [
        "# M=3\n",
        "p_lsq_3 = fitting(M=3)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting Parameters: [ 19.05362997 -27.74343879   8.70678294   0.11715508]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pPlobUcABClF8ycznO0lPgW2fG30LtdpYLJKabuLjtRE0rFaee5tZHFAlCoqL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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RMwfnKgLF7Qa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 323
        },
        "outputId": "0e399fb1-0f8d-45f3-f72c-10de3514f6c0"
      },
      "source": [
        "# M=9\n",
        "p_lsq_9 = fitting(M=9)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fitting Parameters: [ 2.35687617e+04 -1.06903523e+05  2.03079132e+05 -2.09483087e+05\n",
            "  1.27079276e+05 -4.57762852e+04  9.37628698e+03 -9.83860188e+02\n",
            "  4.31804753e+01  2.11312435e-01]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EYW09aFyzCp+vPUFWjgz9FOJGZpz8L4CVDTiWrpxCRnYuU9eeoGmdqjzayvAz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bzjkDkMKF7Qd",
        "colab_type": "text"
      },
      "source": [
        "当M=9时，多项式曲线通过了每个数据点，但是造成了过拟合"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EJUx9DT7F7Qd",
        "colab_type": "text"
      },
      "source": [
        "### 正则化"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NBkSQy5uF7Qe",
        "colab_type": "text"
      },
      "source": [
        "结果显示过拟合， 引入正则化项(regularizer)，降低过拟合\n",
        "\n",
        "$Q(x)=\\sum_{i=1}^n(h(x_i)-y_i)^2+\\lambda||w||^2$。\n",
        "\n",
        "回归问题中，损失函数是平方损失，正则化可以是参数向量的L2范数,也可以是L1范数。\n",
        "\n",
        "- L1: regularization\\*abs(p)\n",
        "\n",
        "- L2: 0.5 \\* regularization \\* np.square(p)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LPueNjlFF7Qe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "regularization = 0.0001\n",
        "\n",
        "def residuals_func_regularization(p, x, y):\n",
        "    ret = fit_func(p, x) - y\n",
        "    ret = np.append(ret, np.sqrt(0.5*regularization*np.square(p))) # L2范数作为正则化项\n",
        "    return ret"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l2hCjmnMF7Qg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 最小二乘法,加正则化项\n",
        "p_init = np.random.rand(9+1)\n",
        "p_lsq_regularization = leastsq(residuals_func_regularization, p_init, args=(x, y))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2SzuO3wTF7Qi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "69382bd4-d969-47d3-fd6f-a04fb39f303a"
      },
      "source": [
        "plt.plot(x_points, real_func(x_points), label='real')\n",
        "plt.plot(x_points, fit_func(p_lsq_9[0], x_points), label='fitted curve')\n",
        "plt.plot(x_points, fit_func(p_lsq_regularization[0], x_points), label='regularization')\n",
        "plt.plot(x, y, 'bo', label='noise')\n",
        "plt.legend()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f23eb43e240>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NOYuvCwUr/8k/LgwsHUBXswOb/KL8mH58Oh62HnzTcRlSbAhsHkYdK30mdijk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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}